The n-fold Darboux transformation (DT) is a 2\times2 matrix for the Kaup-Newell (KN) system. In this paper,each element of expressed by ratio $(n+1)\times (n+1)$ determinant and $n\times n$ eigenfunctions. Using these formulae, expressions $q^{[n]}$ $r^{[n]}$ in KN system are generated DT. Further, under reduction condition, rogue wave,rational traveling solution, dark soliton, bright breather periodic solution derivative nonlinear Schr\"odinger(DNLS) equation given explicitly different seed...

The Fokas-Lenells (FL) equation arises as a model eqution which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order (in Schr\"odinger (NLS) results). Here we present an explicit analytical representation rogue waves of FL equation. This is constructed deriving appropriate Darboux transformation (DT) and utilizing Taylor series expansion associated breather solution. when certain higher-order effects are considered, given.

The rogue waves in a resonant erbium-doped fiber system governed by coupled of the nonlinear Schr\"odinger equation and Maxwell-Bloch (NLS-MB equations) are given explicitly Taylor series expansion about breather solutions normalized slowly varying amplitude complex field envelope $E$, polarization $p$, population inversion $\ensuremath{\eta}$. $n$-order three fields constructed using Darboux transformation (DT) assuming periodic seed solutions. Moreover, determinant forms with $n+3$ free...

We construct higher order rogue wave solutions for the Gerdjikov-Ivanov equation explicitly in term of determinant expression.Dynamics both soliton and non-soliton is discussed.A family with distinct structures are presented, which new to equation.

The Gerdjikov-Ivanov (GI) system of q and r is defined by a quadratic polynomial spectral problem with 2 × matrix coefficients. Each element the n-fold Darboux transformation (DT) for this expressed ratio (n + 1) determinant n eigenfunctions, which implies representation q[n] r[n] generated from known solution r. By choosing some special eigenvalues eigenfunctions according to reduction conditions = −(r[n])*, provides new solutions GI equation. As examples, breather rogue wave are given...

Considering certain terms of the next asymptotic order beyond nonlinear Schrödinger equation, Fokas–Lenells (FL) equation governed by FL system arises as a model for pulse propagation in optical fibers. The expressions q[n] and r[n] are generated n-fold Darboux transformation (DT), each element matrix is 2 × matrix, expressed ratio (2n + 1) determinant 2n eigenfunctions. Further, Taylor series expansion about n-order breather solutions using DT assuming periodic seed under reduction can...

The inverse scattering method is performed to the complex modified Korteweg–de Vries equation with zero boundary condition by developing an appropriate Riemann–Hilbert problem (RHP). We solve RHP when reflection coefficient has multiple higher-order poles, and display formulae of bound-state (BS) solitons BS which correspond one pole respectively. patterns are shown interactions between considered.

We report a novel and new types of rogue optical wave propagation in an erbium-doped fibre system governed by the nonlinear Schrödinger Maxwell–Bloch equation. The breather solutions three fields, namely field envelop, polarization population inversion, are used to generate waves. For first time, we bright and, particular, dark waves coupled systems. distinction between discussed detail through figures. formation our model can also be connected generation supercontinuum resonant fibre.

We consider a two-level atomic system interacting with an electromagnetic field controlled in amplitude and frequency by high intensity laser. show that the of induced electric admits envelope profile corresponding to breather soliton. demonstrate this soliton can propagate any shift respect control laser, except critical frequency, at which undergoes structural discontinuity transforms rogue wave. A mechanism generation waves means intense laser is thus revealed.

In this letter, the designable integrability (DI) of variable coefficient derivative nonlinear Schrödinger equation (VCDNLSE) is shown by construction an explicit transformation which maps VCDNLSE to usual (DNLSE). One novel feature with DI that its coefficients can be designed artificially and analytically using transformation. What more, from rogue wave rational traveling solution DNLSE, we get two kinds waves kind has vanishing boundary condition, other non-vanishing condition. The also...

The mixed nonlinear Schrödinger (MNLS) equation is a model for the propagation of Alfvén wave in plasmas and ultrashort light pulse optical fibers with two effects self-steepening self phase-modulation(SPM), which also first non-trivial flow integrable Wadati-Konno-Ichikawa(WKI) system. determinant representation Tn n-fold Darboux transformation(DT) MNLS presented. smoothness solution q[2k] generated by T2k proved cases (non-degeneration double-degeneration ) through iteration...

The rotating reduced Maxwell-Bloch (RMB) equations, which describe the propagation of few-cycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from system complete equations without using slowly varying envelope approximations. Two hierarchies obtained rational solutions, including rogue waves, also called RMB constructed explicitly through degenerate Darboux transformation. In addition to above, dynamical evolution first-,...

We present a rational solution for mixed nonlinear Schrödinger (MNLS) equation. This has two free parameters, and b, representing the contributions of self-steepening self phase-modulation (SPM) an associated physical system, respectively. It describes five soliton states: paired bright-bright soliton, single bright-grey bright-black rogue wave state. show that transition among these states is induced by SPM through tuning values b. unique potentially fundamentally important phenomenon in...

In this paper, we provide a simple method to generate higher order position solutions and rogue wave for the derivative nonlinear Schr\"odinger equation. The formulae of these are given in terms determinants. dynamics structures generated by studied.

Considering certain terms of the next asymptotic order beyond nonlinear Schrodinger equation (NLS) equation, Fokas-Lenells (FL) governed by FL system arise as a model for pulse propagation in optical fibers. The expressions q[n] and r[n] are generated n-fold Darboux transformation (DT). Further, Taylor series expansion about n-order breather solutions using DT assuming periodic seed under reduction can generate rogue waves explicitly with 2n+3 free parameters.

The magnetization curves along the crystal axes for Gd2Fe17 and Gd2Fe17H3 were analysed based on single-ion model. If Gd–Fe exchange interaction has been taken as isotropic usual, fitted values of magneto-crystalline anisotropy Fe sublattices in would become unreasonably different from those corresponding Y or Lu compounds. It was shown that large difference is caused by neglect interaction.